The term “hit frequency” is generally universally acknowledged in the gaming industry to refer to how often the player receives a payoff of any kind. However, as we discussed in “The Two Kinds of Hit Frequency,” this definition of hit frequency is incomplete, particularly with regard to multi-stage poker games. In such games, betting frequency (the percentage of hands a player can bet) and max-betting frequency (in games with scalable betting, how often the player can bet the max) also serve as positive reinforcement to the gambler, and should be accounted for.

Moreover, even the payoff definition of hit frequency is incomplete, as we really need two categories:

Win frequency: How often the player shows a net win,

Payoff frequency: How often the player receives a payoff of any kind, including net wins, pushes, and fractional pays (a return with a net loss); this is the traditional definition of hit frequency.

The distinction is extremely important. In a game like Pai Gow, for example, the player wins on about 30% of hands and ties on about 40% of hands, for a total payoff frequency – the traditional definition of hit frequency – of about 70%. And so while it’s great that the player gets something back on about 70% of hands, clearly the player feels a lot more strongly about the 30% of hands he shows a win on than the 40% of hands on which he pushes.

The table below shows the win and payoff frequencies for some of the most prominent proprietary table games on the market. In most games, win frequency and payoff frequency are essentially the same, as ties are relatively infrequent in those games. Ties occur on 3.2% of hands in Ultimate Texas Hold’em, which makes sense as a flop game in which the player and dealer share the five community cards.

Mississippi Stud presents a unique case. Mississippi Stud is a straight paytable game – there is no dealer – in which the player pushes if he makes a pair of sixes through tens, and is paid according to a pay table if he makes a pairs of jacks or better. As we noted in our discussion on betting scalability and payoff scalability, Mississippi Stud is unique among current offerings in that it features both scalable betting and scalable payoffs. In fact, the betting is extremely scalable where the player can bet up to 3x on three successive betting rounds, for a total bet of up to 10 units total (including the ante).

The tradeoff is clear, where the game has a relatively low win frequency of 28.6%. This is partially mitigated by the fact that the game pushes when the player makes a pair of sixes through tens, which occurs on 10.2% of hands, for a total payoff frequency of 38.8%.